Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions

Corro, Diego; Galaz-García, Fernando

doi:10.1090/proc/14961

Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions
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by Diego Corro and Fernando Galaz-García PDF

Proc. Amer. Math. Soc. 148 (2020), 3087-3097 Request permission

Abstract:

We show that for each $n\geqslant 1$, there exist infinitely many spin and non-spin diffeomorphism types of closed, smooth, simply-connected $(n+4)$-manifolds with a smooth, effective action of a torus $T^{n+2}$ and a metric of positive Ricci curvature invariant under a $T^{n}$-subgroup of $T^{n+2}$. As an application, we show that every closed, smooth, simply-connected $5$- and $6$-manifold admitting a smooth, effective torus action of cohomogeneity two supports metrics with positive Ricci curvature invariant under a circle or $T^2$-action, respectively.

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